Lorentz contracted geometrical model

Abstract

The model assumes that when two high energy particles collide each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz-contraction in the incident direction. Folding the two spatial distribution together we obtain the slope (b) of the elastic diffraction peak in terms of the c.m. velocities ([beta]i and [beta]j) and the sizes (Ai and Aj) of the two incident particles. These sizes are assumed to have the experimental s-dependence of [sigma]tot [is proportial to] [pi]A2 for each reaction. The combined s-dependence of the [sigma]tot's and the [beta]'s gives the s-dependence of the elastic slope . This formula agrees with the experimental slope for p-p, -p, K+-p, K--p and [pi]+/--p elastic scattering from 3 to 1500 GeV/c, with only 3 parameters: A[pi]2 = 6.1, AK2 = 3.3 and Ap2 = 10.5 (GeV/c)-2.